Abstract:
We study the free energy of mean-field multi-species spin glass models. For such models with D species, the Parisi formula is known to be valid, and expresses the limit free energy as an infimum over monotone probability measures on R^D_+. We show here that one can transform this representation into an infimum over all probability measures on $\R_+^D$ of a convex functional, involving an optimal transport term. We then deduce that the Parisi formula admits a unique minimizer. Using convex-duality arguments, we also obtain a new representation of the free energy as a supremum over martingales in a Wiener space. Based on a joint work in preparation with Victor Issa and Jean-Christophe Mourrat.
Biography:
Hong-Bin Chen is a tenure-track Assistant Professor of Mathematics at NYU Shanghai. He was previously a postdoctoral researcher at the Institut des Hautes Études Scientifiques (IHES). He received his Ph.D. in Mathematics from the Courant Institute of Mathematical Sciences at New York University. His research focuses on probability theory and probabilistic models in statistical physics.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai
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